I've been doing the no-carb diet for 4 weeks and the first 2 and a half weeks were great but now I seem to be staying at the same weight or maybe even going up
a pound and then down a pound on certain days.

Is this my bopdy adjusting to the diet, and will it finally 'give in' to the idea of weight loss?

Your experience is very common. The initial weight loss is usually mostly water, not real fat. When you first go low carb you run down your intermediate energy stores - your glycogen stores - which consist of glucose held in water. As you burn up the glucose, you excrete the water, and the scales show what can often be a very considerable weight loss. This can lull you into a false sense of security, or can be a marvellous motivator to continue the diet, depending on which way you look at it. But once you've run down your glycogen stores, the water loss stops, and very often, the weight loss seems to stop for a while. Your body should now start burning off your long term fat stores, but this may happen painfully slowly for some people. That's when you've got to just have faith and 'hang in there'. Not easy when you're trying hard and getting no apparent reward for your efforts, I know. I've been there many times myself!

One thing to keep in mind is the issue of muscle. Muscle is denser and therefore 'weighs heavier' than the same volume of fat. If you've been stepping up your exercise, particularly if you have been lifting weights, you may well have been replacing fat with muscle. If that's the case, then the scales may not show a result but the tape measure will. Replacing fat with muscle is very important for long term dieting success so if this is what's happening, then you ARE getting results.

Another facet of weight loss is that your fat cells sometimes try to replace the fat they've lost with the only other material available to them - water. It can take weeks, even months sometimes for your body to decide to release that water, producing an unexpected but sometimes long awaited loss on the scales.

You may be interested in my book 'Why Can't I lose weight' at http://www.dietplateau.com. This gives a lot more detail on the many reasons why you might not be losing (or appear to be losing) weight, and helps you create a personal action plan to identify and overcome your own personal barriers to weight loss.